How long will it take to collect 1.0 L of H2(g) at STP in the electrolysis of 2.0 M HCl with a current of
4.25 A?
a. 15 min
b. 34 min
c. 2.8 hr
d. 11 hr
To determine the time required to collect 1.0 L of H2(g) at standard temperature and pressure (STP) in the electrolysis of 2.0 M HCl with a current of 4.25 A, we need to use Faraday's laws of electrolysis.
First, we need to calculate the number of moles of H2 produced. The balanced equation for the electrolysis of water is:
2HCl(aq) + 2e- -> H2(g) + 2Cl-(aq)
From the equation, we can see that for every 2 electrons (2e-) transferred, we produce 1 mole of H2(g).
Next, we calculate the number of moles of electrons (n) transferred using the current (I) and time (t). The formula is:
n = It / F
Where:
- n is the number of moles of electrons
- I is the current in amperes (A)
- t is the time in seconds (s)
- F is Faraday's constant, which is approximately 96,485 C/mol e-
To find the number of moles of H2(g) produced, we need to divide the number of moles of electrons by 2 (since 2 electrons are required to produce 1 mole of H2(g)).
Next, we can calculate the volume of H2(g) produced using the ideal gas law equation:
PV = nRT
Where:
- P is the pressure of the gas (STP has a pressure of 1 atm)
- V is the volume of the gas in liters (L)
- n is the number of moles of the gas
- R is the ideal gas constant, which is approximately 0.0821 L·atm/(mol·K)
- T is the temperature of the gas in Kelvin (K) (STP has a temperature of 273.15 K)
Finally, we compare the calculated volume of H2(g) to the desired volume of 1.0 L. The time required to reach this volume will depend on the current used.
Now, let's go through the calculations step by step:
1. Calculate the number of moles of electrons (n) transferred.
n = It / F
n = (4.25 A) x (t s) / (96,485 C/mol e-)
2. Calculate the number of moles of H2(g) produced.
Moles of H2 = n / 2
3. Calculate the volume of H2(g) produced.
V = (n / 2) x (0.0821 L·atm/(mol·K)) x (273.15 K) / (1 atm)
4. Compare the calculated volume of H2(g) to the desired volume of 1.0 L and solve for the time (t).
Once you have calculated the volume of H2(g) produced, it's important to compare it to the desired volume of 1.0 L and select the corresponding time option from the given choices.